Jessica is 8 years older than Vanessa. Fifteen years ago, Jessica was 5 times as old as Vanessa. How old is Vanessa now?
We can use the given information to write down two equations that describe the ages of Jessica and Vanessa. Let Jessica's current age be $j$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $j = v + 8$ Fifteen years ago, Jessica was $j - 15$ years old, and Vanessa was $v - 15$ years old. The information in the second sentence can be expressed in the following equation: $j - 15 = 5(v - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = v + 8$ . Substituting this into our second equation, we get the equation: $(v + 8)$ $-$ $15 = 5(v - 15)$ which combines the information about $v$ from both of our original equations. Simplifying both sides of this equation, we get: $v - 7 = 5 v - 75$ Solving for $v$ , we get: $4 v = 68$ $v = 17$.